The grades on a history midterm at Loyola are normally distributed with $\mu = 75$ and $\sigma = 2.5$. William earned a $68$ on the exam. Find the z-score for William's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for William's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{68 - {75}}{{2.5}}} $ ${ z \approx -2.80}$ The z-score is $-2.80$. In other words, William's score was $2.80$ standard deviations below the mean.